Hanson Wagner
06/13/2024 · High School
A boat sails directly toward a \( 300-\mathrm{m} \) skyscraper that stands on the edge of a harbor. The angular size of the building is the angle formed by lines from the top and bottom of the building to the observer (see figure). Complete parts a and \( b \) below. a. Use a trigonometric equation to find an expression for the angle, \( \theta \), in terms of x . (Type an equation.) b. What is the rate of change of the angular size, \( \frac{\mathrm{d} \theta}{\mathrm{dx}} \), when the boat is \( \mathrm{x}=350 \mathrm{~m} \) from the building? rad/m (Round to five decimal places as needed.)
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a. \(\theta = \tan^{-1}\left(\frac{300}{x}\right)\)
b. \(\frac{d\theta}{dx} \approx -0.00141 \, \text{rad/m}\)
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